We find the greatest value 𝑝 and the least value 𝑞 in 0,1-2 such that the double inequality 𝐻𝑝𝑎+1−𝑝𝑏,𝑝𝑏+1−𝑝𝑎0 with 𝑎≠𝑏. Here, 𝐻𝑎,𝑏, and 𝐼𝑎,𝑏 denote the harmonic and identric means of two positive numbers 𝑎 and 𝑏, respectively.